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In 1865, James Clerk Maxwell assembled all the known "Laws"
of in their most compact, elegant (differential) form,
shown here in SI units:
GAUSS' LAW FOR ELECTROSTATICS:
![\begin{displaymath}\Div{D} \; = \; \rho
\end{displaymath}](img43.gif) |
(22.9) |
GAUSS' LAW FOR MAGNETOSTATICS:
![\begin{displaymath}\Div{B} \; = \; 0
\end{displaymath}](img44.gif) |
(22.10) |
FARADAY'S LAW:
![\begin{displaymath}\Curl{E} +
{\partial \Vec{B} \over \partial t} \; = \; 0
\end{displaymath}](img45.gif) |
(22.11) |
AMPÈRE'S LAW:
![\begin{displaymath}\Curl{H} -
{\partial \Vec{D} \over \partial t}
\; = \; \Vec{J}
\end{displaymath}](img46.gif) |
(22.12) |
These four basic equations are known collectively
as MAXWELL'S EQUATIONS; they are considered by most Physicists
to be a beautifully concise summary of phenomenology.
Well, actually, a complete description of
also requires two additional laws:
EQUATION OF CONTINUITY:
![\begin{displaymath}{\partial \rho \over \partial t} \; = \; - \Div{J}
\end{displaymath}](img47.gif) |
(22.13) |
LORENTZ FORCE:
![\begin{displaymath}\Vec{F} \; = \; q \, \left( \Vec{E} \; + \;
\Vec{v} \times \Vec{B} \right) .
\end{displaymath}](img48.gif) |
(22.14) |
Next: The Wave Equation
Up: Maxwell's Equations
Previous: Ampère's Law
Jess H. Brewer -
Last modified: Wed Nov 18 12:32:37 PST 2015